Here, we will discuss the analytical formulation of a dynamical
variable characterized as structure scalar, which can be utilized to
compute the structural complexity of self-gravitating celestial
systems. This dynamical variable is described as the complexity
factor \((\mathbb {C}_{\mathbf {F}})\)  [1]}. We will
examine the cosmological impact on the \((\mathbb {C}_{\mathbf {F}})\) 
of large-scale self-gravitating structures with \(\alpha \mathcal {G}^{n}(\beta \mathcal {G}^{m}+1)+\eta \mathbf {T}^{2}\) 
corrections and study the implications of \(\mathrm {GR}\)  at
large-scales. The fundamental mechanism to split up the Riemann
tensor orthogonally to obtain some dynamical variables (structure
scalars), was formerly presented by Bel [2]}.
Afterward, Herrera
[3]}, [4]} deployed this
mechanism and employed this approach to study several problems
corresponding to the structural and evolutionary features of
gravitational compact systems in \(\mathrm {GR}\) . These scalar
variables are particularly significant to our discussion, since one
of these scalars appear to assess the complexity of gravitational
compact systems [5]}.
